# Canzani, Yaiza

Professor

Director of Graduate Studies

Phillips Hall 305

canzani@email.unc.edu

Website

## Research Interests

Partial differential equations, semiclassical analysis, mathematical physics, spectral theory, differential geometry

## Professional Background

BS. Universidad de la República, Uruguay, 2008; Ph.D. McGill University, Montreal, 2013; Member of the Institute for Advanced Study, Princeton, 2014-2015; Benjamin Peirce Fellow, Harvard University, Boston, 2013-2016

## Research Synopsis

Canzani's research focuses on understanding the behavior of Laplace eigenfunctions, φ_{λ}, using techniques of harmonic analysis, spectral theory, geometric analysis, microlocal analysis, probability, and dynamical systems. From a quantum mechanics point of view, |φ_{λ}(*x*)|^{2} represents the probability for finding a quantum particle of energy λ^{2} at the point >(*x*. As a result, understanding how φ_{λ} concentrates is a crucial problem for the mathematical physics community. Most of Canzani's research concerns the high energy regime λ→∞.

## Representative Publications

*Topology and Nesting of the Zero Set Components of Monochromatic Random Waves*

Y. Canzani and P. Sarnak.,

Communications on Pure and Applied Mathematics, 72 , 2, 343-374, 2019

*On the Growth of Eigenfunction Averages: Microlocalization and Geometry*

Y. Canzani and J. Galkowski.,

Duke Mathematical Journal, 168, 16, 2991-3055, 2017

*Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law*

Y. Canzani and B. Hanin.,

Analysis and Partial Differential Equations, 8, 7, 1707-1731, 2015